Question

if the circumference of the base of cylinder is
44cm and the sum of its radius and height is
27 cm, find its total surface area.​

Answer 1

EXPLANATION.

Circumference of the base of cylinder = 44.

Sum of its radius and height = 27 cm.

As we know that,

Circumference of the base of cylinder = 2πr.

⇒ 2πr = 44.

⇒ 2 x 22/7 x r = 44.

⇒ 2 x 22 x r = 44 x 7.

⇒ 44 x r = 44 x 7.

⇒ r = 7 cm.

Sum of its radius and height = 27 cm.

⇒ r + h = 27.

⇒ 7 + h = 27.

⇒ h = 27 - 7.

⇒ h = 20 cm.

As we know that,

Formula of :

Total surface area = 2πr(r + h).

⇒ 2 x 22/7 x 7 (7 + 20).

⇒ 2 x 22 (27).

⇒ 2 x 22 x 27.

⇒ 1188cm².

                                                                                                                       

MORE INFORMATION.

(1) = Volume of cylinder = πr²h.

(2) = Volume of cuboid = L x B x H.

(3) = Volume of cube = a³.

(4) = Volume of cone = 1/3πr²h.

(5) = Volume of sphere = 4/3πr³.

(6) = Volume of hemisphere = 2/3πr³.

Answer 2

Answer:

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ Given:}}}}}}}}\end{gathered}$

• ➲ Circumference of the base of Cylinder = 44 cm
• ➲ Sum of radius and height if Cylinder = 27 cm

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ To Find:}}}}}}}}\end{gathered}$

• ➲Total surface area

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ Using Formula:}}}}}}}}\end{gathered}$

${\dag{\underline{\boxed{\sf{Circumference \: of \: Cylinder =2{\pi}r}}}}}$

$\dag{\underline{\boxed{\sf{Total \: surface \: area \: of \: Cylinder = 2{\pi}r(h + r), }}}}$

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ Diagram:}}}}}}}}\end{gathered}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{r}}\put(9,17.5){\sf{h}}\end{picture}$

• Request: See the diagram from website Brainly.in.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ Solution:}}}}}}}}\end{gathered}$

${\dag{\underline{\underline{\frak{\green{Let \: the \: : }}}}}}$

• Radius of Cylinder = r
• Height of Cylinder = h

$\begin{gathered}\end{gathered}$

${\dag{\underline{\underline{\frak{\green{Finding \: the \: radius \: of \: Cylinder. \: : }}}}}}$

According to the question,

$\quad{: \implies{\sf{Circumference \: of \: Cylinder =2{\pi}r}}}$

• Substituting the values

$\begin{gathered}\quad{: \implies{\sf{44 =2 \times {\dfrac{22}{7}} \times r}}} \\ \\ \quad{: \implies{\sf{44 ={\dfrac{44}{7}} \times r}}} \\ \\ \qquad{: \implies{\sf{44 \times {\dfrac{7}{44}} = r}}} \\ \\ \qquad{: \implies{\sf{\cancel{44} \times {\dfrac{7}{\cancel{44}}} = r}}} \\ \\ \qquad{: \implies{\sf{7 = r}}} \\ \\\qquad\dag{\underline{\boxed{\sf{\purple{r = 7\: cm}}}}}\end{gathered}$

• Hence, The radius of cylinder is 7 cm

$\begin{gathered}\end{gathered}$

${\dag{\underline{\underline{\frak{\green{Finding \: the \: height \: of \: Cylinder \: : }}}}}}$

According to the question,

$\quad{: \implies{\sf{radius + height = 27 cm}}}$

• Substituting the values

$\begin{gathered}\quad{: \implies{\sf{7 + height = 27 cm}}} \\ \\ : \implies{\sf{ height = 27 - 7}} \\ \\ : \implies{\sf{ height = 20 \: cm}} \\ \\ \dag{\underline{\boxed{\sf{\purple{ height = 20 \: cm}}}}}\end{gathered}$

• Hence, The height of Cylinder is 20 cm.

$\begin{gathered}\end{gathered}$

${\dag{\underline{\underline{\frak{\green{Now \: Finding \: the \: total \: surface \: area \: of \: Cylinder \: : }}}}}}$

$\begin{gathered} \quad{ : \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2{\pi}r(h + r)}}} \end{gathered}$

• Substituting the values

$\begin{gathered} \quad{ : \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2 \times { \dfrac{22}{7}} \times 7(20 + 7)}}} \\ \\ \qquad{: \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2 \times { \dfrac{22}{7}} \times 7(27)}}} \\ \\ \qquad{: \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2 \times { \dfrac{22}{7}} \times 7 \times 27}}} \\ \\ \qquad{: \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2 \times { \dfrac{22}{\cancel{7}}} \times \cancel{7} \times 27}}} \\ \\ \qquad{: \implies{\sf{Total \: surface \: area \: of \: Cylinder = 2 \times 22 \times 27}}} \\ \\ \qquad{: \implies{\sf{Total \: surface \: area \: of \: Cylinder = 1188 \: {cm}^{2}}}} \\ \\ \qquad\dag{ \underline{\boxed{\sf{\purple{Total \: surface \: area \: of \: Cylinder = 1188 \: {cm}^{2}}}}}}\end{gathered}$

• Henceforth,The Total surface area of Cylinder is 1188 cm².

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\underline{\underline{\maltese{\large{\textsf{\textbf{\red{ Learn More:}}}}}}}}\end{gathered}$

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$